Parameters of the proposed model. Reproduced from Ogawa et al. 2006 with permission.

using the swimming velocity measured in past experiments. The terminal velocity of a cell was obtained by substituting Z = 0 into the equation of motion under the conditions ^ = 0: Z = F/D — efn\x^\(i)=o/3nnR. Since Xa equals / at (^ = 0, we can estimate fn from: fn = 3KIIR\X\/L Measure-ment of the cell velocity by using a high-speed tracking system, described later in section 4.3, gave a velocity of around 400|am/s. Using this value, we estimated fn to be 4.71 x 10"^ N/m. In addition, we adjusted the parameter 5 to be 7.5 based on experimental data of the cell trajectories obtained by our system (Ogawa et al. 2005). Next, we tested whether our proposed model could exhibit this phenomenon like real cells. When an electric field is applied in the direction opposite to the swim-ming direction of a cell, the cell makes a U-turn motion. We chose this behavior for the test. Swimming trajectories for cells with eleven differ-ent initial orientations were calculated. Figure 3 shows all trajectories si-multaneously. All cells were configured to have the same initial position, namely, at the origin (0,0), but their initial angles (f> differed by intervals of 30°(-150°, -120°,..., 150°). An electric field of 5.0 V/cm was applied along the X-axis. The trajectory of each cell was calculated by solving or-dinary differential equations. As shown in Fig. 3, all cells starting from the origin turned toward the cathode, like real cells. It is interesting that real-istic macroscopic behavior emerged from a microscopic description of the ciliary motion.

Real-Time Observation System and Wet Experiments

 

in this section, we describe a novel system for real-time continuous obser-vation of galvanotaxis using a visual tracking method. With this system, 

Simulation of U-turn motions of cells. Reproduced from Ogawa et al. 2006 with permission. 

we verified the validity of the model using these data. 

Why Tracking

To realize precise observation of freely swimming cells, it is necessary to perform continuous observation of rapidly swimming, non-immobilized cells, to provide a sufficiently large working area, and to perform detailed observation of a specific cell with high magnification to precisely control its actuation. We found, however, that most conventional microscope systems could not satisfy these demands. To overcome these obstacles, we adopted a specially designed tracking method. In this article, we mainly use the term "tracking" in the sense that the camera pursues a target so as to keep it always in the center of the visual field (sometimes we also call it "lock-on tracking"). As shown in Fig. 4, a lock-on mechanism can be realized by moving the position of the specimen on a stage so that the camera always keeps the target at the center

Lock-on tracking scheme. The camera pursues a target so as to keep it always in the center of the visual field. Reproduced fi*om Ogawa et al. 2005 with permission

System Configuration   

Our system measures the cell position and angle continuously at a 1-kHz frame rate, using a high-speed lock-on tracking method. The configuration of the overall system and its block diagram are illustrated in Fig. 5. An electrical stimulus is applied to cells swimming in a chamber placed on an electrical stimulus input device mounted on an XY stage. The stage is controlled by a high-speed vision system so as to keep a cell in the center of the field of view. The position and orientation of the cell are calculated from image features. More details of this system can be found in our previous work (Ogawa et al. 2005). The I-CPV vision system (Toyoda et al. 2001) is mounted on an upright optical microscope (Olympus, BX50WI) and captures dark-field images at 1-kHz frame rate. From the captured images, the I-CPV calculates image moments and sends them to the PC. They are used for calculating the at-titude and the position of the target. Figure 5 C shows an example of the

Example of trajectory and orientation of a cell reconstructed by the real-time galvanotaxis observat

ion system. Reproduced from Ogawa et al. 2005 with permission.  

 tracked image of a Paramecium cell making a U-turn. The PC controls the position of the chamber fixed on the XY stage (SMC, LAL00-X070) by sending instructions to the stage, in order to keep the specimen at the center ofthe visual field. In the electrical stimulus input device, tw^o carbon electrodes of 0.5-mm diameter are placed 22-mm apart in parallel on a glass slide to allow control ofthe electrical stimulus in one direction. The specimen chamber, which is 0.17-mm deep, is placed between the electrodes. The PC provides a voltage in the range0 V to the electrodes via a D/A converter board (Interface, PCI-3310). The whole system is controlled at a frequency of 1 kHz by the PC running a real-time OS (800 MHz, ART-Linux). Figure 6 shows an example ofthe trajectory and orientation of a swimming Paramecium cell reconstructed by the real-time galvanotaxis observation system. In this experiment, the electric field was applied leftward during 0-6 s, then rightward during 6-12 s, and leftward again during 12-18s

  Experiment 

Experimental data were obtained by high-speed measurement of the re-sponses of a single cell to an electric field, using the real-time galvanotaxis observation system. Wild-type P. caudatum cells were cultured at 20-25°C in a soy flour solution. Cells grown to the logarithmic or stationary phase

 Comparison between simulated data (left) and experimental data (right) in the U-turn motion. Only the X-coordinates (positions along the electric field) were extracted. Experimental and artificial data for three seconds fi-om the application of a stimulus in six trials are overlaid. Each number indicates a couple of data sharing the same initial angle. The figure indicates that the simulated data was approximately in agreement with the experimental results

were collected together with the solution, fil-tered through a nylon mesh to remove debris, and infused into a chamber. A DC electric field with a step-like temporal profile rising to 4.1 V/cm was applied to the cells. We compared simulated and experimental positions in the U-turn motion. We extracted positions along the electric field (X direction), because X-disposition is almost independent of fluctuations caused by spiral motions, which we disregarded. Figure 7 shows experimental data (right) for three seconds from applica-tion of a stimulus (reversal of the electric field) in six trials. In the sim-ulation (left), the initial angle in each trial was set to the same value in the measured data. The field strength was set to 4.1 V/cm, the same as in the wet experiment. The figure indicates that the simulated data was ap-proximately in agreement with the experimental results. A more rigorous comparison will require three-dimensional tracking (Oku et al. 2006), and 3-D experiments are currently underway in our laboratory

  Conclusion 

In this article, we have proposed a physical model of Paramecium galvan-otaxis using a bottom-up approach to link the microscopic ciliary motion and the macroscopic behavior of a cell. We investigated the validity of the model by numerical experiments using a novel observation system.